# A Cross-Domain Graph Learning Protocol for Single-Step Molecular Geometry Refinement

arXiv: https://arxiv.org/abs/2601.22723 · HTML: https://mlsanity.com/paper/2601.22723/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 56 references that are in the map.
- First posted on arXiv 30 Jan 2026.

## Builds on (most cited first, 22 of 22)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation](https://mlsanity.com/paper/2203.02923/) (2022)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [Torsional Diffusion for Molecular Conformer Generation](https://mlsanity.com/paper/2206.01729/) (2022)
- [Machine Learning Force Fields](https://mlsanity.com/paper/2010.07067/) (2020)
- [ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Prediction](https://mlsanity.com/paper/2106.06130/) (2021)
- [Learning Gradient Fields for Molecular Conformation Generation](https://mlsanity.com/paper/2105.03902/) (2021)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [GeoMol: Torsional Geometric Generation of Molecular 3D Conformer Ensembles](https://mlsanity.com/paper/2106.07802/) (2021)
- [UMA: A Family of Universal Models for Atoms](https://mlsanity.com/paper/2506.23971/) (2025)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://mlsanity.com/paper/2205.06643/) (2022)
- [Learning Neural Generative Dynamics for Molecular Conformation Generation](https://mlsanity.com/paper/2102.10240/) (2021)
- [A Generative Model for Molecular Distance Geometry](https://mlsanity.com/paper/1909.11459/) (2019)
- [A new perspective on building efficient and expressive 3D equivariant graph neural networks](https://mlsanity.com/paper/2304.04757/) (2023)
- [Diffusion-based Generative AI for Exploring Transition States from 2D Molecular Graphs](https://mlsanity.com/paper/2304.12233/) (2023)
- [3DReact: Geometric deep learning for chemical reactions](https://mlsanity.com/paper/2312.08307/) (2023)

## Built on by (most cited first, 1 of 1)

- [Hypothesis-and-Refinement Learning of Organic Structures from Multimodal Spectroscopic Data](https://mlsanity.com/paper/2607.19816/) (2026)

## Abstract (arXiv)

Accurate molecular geometries are a prerequisite for reliable quantum-chemical predictions, yet density functional theory (DFT) optimization remains a major bottleneck for high-throughput molecular screening. Here we present GeoOpt-Net, a multi-branch SE(3)-equivariant geometry refinement network that predicts DFT-quality structures at the B3LYP/TZVP level of theory in a single forward pass starting from inexpensive initial conformers generated at a low-cost force-field level. GeoOpt-Net is trained using a two-stage strategy in which a broadly pretrained geometric representation is subsequently fine-tuned to approach B3LYP/TZVP-level accuracy, with theory- and basis-set-aware calibration enabled by a fidelity-aware feature modulation (FAFM) mechanism. Benchmarking against representative approaches spanning classical conformer generation (RDKit), semiempirical quantum methods (xTB), data-driven geometry refinement pipelines (Auto3D), and machine-learning interatomic potentials (UMA) on external drug-like molecules demonstrates that GeoOpt-Net achieves sub-milli-AA all-atom RMSD with near-zero B3LYP/TZVP single-point energy deviations, indicating DFT-ready geometries that closely reproduce both structural and energetic references. Beyond geometric metrics, GeoOpt-Net generates initial guesses intrinsically compatible with DFT convergence criteria, yielding nonzero ``All-YES'' convergence rates (65.0% under loose and 33.4% under default thresholds), and substantially reducing re-optimization steps and wall-clock time. GeoOpt-Net further exhibits smooth and predictable energy scaling with molecular complexity while preserving key electronic observables such as dipole moments. Collectively, these results establish GeoOpt-Net as a scalable, physically consistent geometry refinement framework that enables efficient acceleration of DFT-based quantum-chemical workflows.